Problem: $K$ is the midpoint of $\overline{JL}$ $J$ $K$ $L$ If: $ JK = 2x + 4$ and $ KL = 4x - 8$ Find $JL$.
A midpoint divides a segment into two segments with equal lengths. ${JK} = {KL}$ Substitute in the expressions that were given for each length: $ {2x + 4} = {4x - 8}$ Solve for $x$ $ -2x = -12$ $ x = 6$ Substitute $6$ for $x$ in the expressions that were given for $JK$ and $KL$ $ JK = 2({6}) + 4$ $ KL = 4({6}) - 8$ $ JK = 12 + 4$ $ KL = 24 - 8$ $ JK = 16$ $ KL = 16$ To find the length $JL$ , add the lengths ${JK}$ and ${KL}$ $ JL = {JK} + {KL}$ $ JL = {16} + {16}$ $ JL = 32$